The present invention relates to an apparatus for obtaining a tomogram of a living body by utilizing the nuclear magnetic resonance phenomenon, and more particularly to an image constructing device suited to take out chemical shift components from measured resonance signals and to form a tomogram of each chemical shift component, by a high-speed imaging method in which a resonance signal is measured in a state that the strength of a gradient magnetic field is varied with time. Incidentally, the image construction means that a tomogram is constructed from a measured resonance signal.
A method of forming a tomogram of each chemical shift component in the magnetic resonance imaging (hereinafter referred to as "MRI") is described in, for example, an article entitled "Chemical-Shift Imaging with Large Magnetic Field Inhomogeneity " (Magnetic Resonance in Medicine, Vol. 4, No. 5, 1987, pages 452 to 460). In this method, resonance signals are measured at some different periods of time in a state that the strength of a gradient magnetic field is kept constant, tomograms of an object are constructed from measured resonance signals by the two-dimensional Fourier transformation method, and tomograms corresponding to chemical shift components are separated from the constructed tomograms. In more detail, each of the chemical shift components is slightly different in resonance frequency from each other. Thus, when a resonance signal is measured at different periods of time, tomograms corresponding to the chemical shift components are different from each other in phase, that is, in the state of nuclear spin. Further, image processing is carried out so that tomograms corresponding to undesired chemical shift components cancel each other on the basis of the above phase difference, to obtain tomograms each formed of a single chemical shift component.
While, a novel imaging method is described in, for example, an article entitled "A Novel Fast Scanning System" (Proceedings of 5th Society of Magnetic Resonance in Medicine, 1986, pages 156 and 157). In this method, a resonance signal is measured in a state that the strength of a gradient magnetic field is varied with time. As a result, the resonance signal can be continuously measured, and thus a time necessary for imaging can be shortened in a great degree.
However, the art concerning this method has given no consideration to the matter that tomograms due to chemical shift components may be constructed, by using a time-varying gradient magnetic field.
Now, let us express the tomogram formed of the i-th chemical shift component by .rho..sub.i (x, y), where x and y designate two-dimensional coordinate values on the tomogram, with the origin at the center of a field of view. Further, let us express the deviation of a resonance frequency of each chemical shift component from a reference frequency by .DELTA..omega..sub.i. It is to be noted that the reference frequency means the resonance frequency of each chemical shift component under a static magnetic field. Then, the resultant resonance signal S(t) of respective resonance signals of chemical shift components is given by the following equation: ##EQU1## Further, G.sub.x and G.sub.y indicate the strength of x- and y-gradient magnetic fields, respectively, .gamma.: a nuclear magnetogyric ratio, and C: a constant.
The inhomogeneity of static magnetic field and the T.sub.2 effect (namely, transverse relaxation time effect) have no connection with the following explanation, and hence explanation thereof will be omitted. Now, let us consider a case where G.sub.x and G.sub.y are constant as in the two-dimensional Fourier transformation method, for example, a case where G.sub.x (t)=G.sub.x.sup.o (namely, a constant) and G.sub.y (t)=O the resonance signal S(t) is rewritten as follows: ##EQU2## Thus, tomograms formed of different chemical shift components are deviated from each other by an amount equal to .DELTA..omega..sub.i / G.sub.x.sup.o. As a result, an overlapping tomogram is formed. In a case where G.sub.x and G.sub.y vary with time, however, signal components due to different chemical shift components do not appear as signal components which are merely deviated from each other, but interact on each other in a complicated manner. Thus, it is impossible to construct tomograms corresponding to chemical shift components at the same time. That is, the conventional chemical shift imaging method is inapplicable to a case where G.sub.x and G.sub.y vary with time.